Errors while Loading Most Recent Version of jQuery

According to this article:

“hover” pseudo-event

As of 1.9, the event name string “hover” is no longer supported as a
synonym for “mouseenter mouseleave”. This allows applications to
attach and trigger a custom “hover” event. Changing existing code is a
simple find/replace, and the “hover” pseudo-event is also supported in
the jQuery Migrate plugin to simplify migration.

If you need to continue using hover() you may use the Migrate plugin.

Change your function to:

function RegisterJQuery()
{
    wp_deregister_script( 'jquery' );
    wp_register_script( 'jquery', '//ajax.googleapis.com/ajax/libs/jquery/1.9.1/jquery.min.js', false, "1.9.1" );
    wp_enqueue_script( 'jquery' );
    wp_register_script( 'migrate', 'http://code.jquery.com/jquery-migrate-1.1.1.min.js');
    wp_enqueue_script( 'migrate' );
}